The `+3` ion of which one of the following has half filled `4f` subshell?

Options

A. `La`
B. `Lu`
C. `Gd`
D. `Ac`

Answer

To determine which +3 ion has a half-filled 4f subshell, we need to analyze the electronic configurations of the given elements in their +3 oxidation state. Let's go through each option step by step.

### Step 1: Identify the electronic configuration of each element.

1. **Lanthanum (La)**:
- Atomic number: 57
- Electronic configuration: [Xe] 6s² 5d¹ 4f⁰

2. **Lutetium (Lu)**:
- Atomic number: 71
- Electronic configuration: [Xe] 6s² 5d¹ 4f¹⁴

3. **Gadolinium (Gd)**:
- Atomic number: 64
- Electronic configuration: [Xe] 6s² 5d¹ 4f⁷

4. **Actinium (Ac)**:
- Atomic number: 89
- Electronic configuration: [Rn] 7s² 6d¹ 5f⁰

### Step 2: Determine the electronic configuration in the +3 oxidation state.

1. **Lanthanum (La) +3**:
- Loses 3 electrons: [Xe] 6s⁰ 5d⁰ 4f⁰
- 4f subshell: 0 electrons (not half-filled)

2. **Lutetium (Lu) +3**:
- Loses 3 electrons: [Xe] 6s⁰ 5d⁰ 4f¹¹
- 4f subshell: 14 electrons (completely filled)

3. **Gadolinium (Gd) +3**:
- Loses 3 electrons: [Xe] 6s⁰ 5d⁰ 4f⁴
- 4f subshell: 7 electrons (half-filled)

4. **Actinium (Ac) +3**:
- Loses 3 electrons: [Rn] 7s⁰ 6d⁰ 5f⁰
- 4f subshell: 0 electrons (not half-filled)

### Step 3: Identify which element has a half-filled 4f subshell.

From the analysis:
- **Lanthanum**: 4f⁰ (not half-filled)
- **Lutetium**: 4f¹⁴ (not half-filled)
- **Gadolinium**: 4f⁷ (half-filled)
- **Actinium**: 4f⁰ (not half-filled)

### Conclusion:
The +3 ion of **Gadolinium (Gd)** has a half-filled 4f subshell.

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